Proportionality and Envy-Free Allocation
Now let’s look at situations in which a set of items is to be divided among players, but in these applications the items themselves must be kept whole. Instead of cake, or plots of land, we are now dealing with individual objects, such as family heirlooms that might be part of an estate that is being contested.
The Knaster-Steinhaus Procedure
In 1948 the Polish mathematician Hugo Steinhaus published the details of a procedure to fairly assign a number of contested items. He attributed the work to his colleague, Bronislaw Knaster. We will assume that each player can monetarily evaluate each of the items in the set to be divided up.
The subject of fair division was initiated during World ...